Inhaltsverzeichnis

Development of
Algorithmic Constructions
12:21:33
Deutsch
19.Apr 2024
<< 113 127 131 >>

odd number < 10000 :
0+i
^20+i
^28+8i
^221+24i
^225+30i40+59i
^27+29i34+49i15+41i46+60i
^22+39i42+53i5+22i9+38i19+23i32+45i27+62i26+50i
^219+20i8+58i10+36i13+46i16+39i57+59i2+54i35+60i3+25i30+49i29+38i28+55i34+42i27+63i40+47i56+61i


The complex number are calculated by exponentation from the botton to the top modulo the input number.

I have sorted the complex numbers: b>a, otherwise I have replaced (a,b) by (b,a)

The listed green complex numbers have norm (a,b)=a²+b²=1 mod p
The listed red complex numbers have norm (a,b)=a²+b²=-1 mod p

The factorisation depends of the number modulo 4:
Let p be an odd prime, then
for p = 1 mod 4 the factorisation depends on p-1
for p = 3 mod 4 the factorisation depends on p+1

The green elements a+bi are quadratic residues and have jacobi (a²+b², f)=1
The red elements a+bi are non quadratic residues and have jacobi (a²+b², f)=-1